Answer
$$0$$
Work Step by Step
We are given that $F(x,y)=(x,y)$
Also, the curve is $r(t)= (4 \cos t, 4 \sin t)$
This implies that $r'(t) = (-4 \sin t, 4 \cos t)$
Therefore, the integral is:
$\oint F \ dr=\int_0^{2 \pi} F[r(t)] r'(t) \ dt\\=\int_0^{2 \pi} (4 \cos t, 4 \sin t) (-4 \sin t, 4 \cos t)\\=\int_0^{2 \pi} 0 \ dt \\=0 $
